Optimal spatial sampling interval for damage detection by curvature or strain energy mode shapes
Optimal spatial sampling interval for damage detection by curvature or strain energy mode shapes
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发表时间：
2004
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通讯作者：
E. Sazonov;P. Klinkhachorn
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作者：
E. Sazonov;P. Klinkhachorn
这项工作致力于提出和应用一种新的方法来估计线性物理模型，该线性物理模型由满阶质量、刚度和阻尼阵表示，能够复制不完整模型的动力学行为。由于不对阻尼阵作任何假设，因此该程序适用于任何线性粘滞阻尼器模型。结果表明，如果所考虑的振型数满足一定的自由度数限制，则该问题有无穷多个不同于其外源特征值的解。通过控制它们对模型在感兴趣的频率范围内的动态行为的影响，得到了适当的最终解。将该方法应用于一个三自由度离散模型和一个离散悬臂梁。在频域和时间域进行了比较，结果表明，该方法提供的物理模型能够准确地复制不完全模型的动态行为。即使对于不满足可解条件的完整模型，该方法在某些情况下也能提供有意义的结果。为了证明估计模型的有效性，在两个算例的一个自由度上增加了一个质量，以表明它们再现了与原始修改后的模型相同的效果。最后，为了重现性，本文中提供的所有模型和算法都已公开提供。
This work is devoted to presenting and applying a novel methodology that estimates a linear physical model, represented by full-rank mass, stiffness and damping matrices, capable of replicating the dynamic behaviour of an incomplete modal model. No hypothesis is made with respect to the damping matrix, so the procedure is applicable assuming any linear viscous damping model. It is shown that, if the number of considered modes satisfies a certain restriction with respect to the number of degrees of freedom, the problem has infinite solutions that differ in their exogenous eigenvalues. By controlling their effect on the dynamic behaviour of the model in the frequency range of interest, a proper final solution is obtained. The methodology is applied to a three-degrees-of-freedom discrete model and a discretized cantilever beam. Comparisons are made in both frequency and time domains which reveal that the methodology provides physical models that accurately replicate the dynamic behaviour of the incomplete modal model. Even for complete models, where the solvability condition is not met, the methodology manages to provide meaningful results in some situations. To prove the usefulness of the estimated models, a mass is added on one DOF of both examples to show that they reproduce the same effects as the original modified ones. Finally, in the interests of reproducibility, all models and algorithms presented in this article have been made publicly available.